Joint Sparsity and Inverse Source for Three-dimensional Shape Estimation of Unknown Targets

Abstract

The reconstruction of qualitative information about unknown obstacles (i.e., presence, location and shape), starting from the measurements of their scattered fields when illuminated with known incident field, takes on great importance in many testing and diagnostics applications, especially in underground prospecting and biomedical imaging. The approaches which aim at solving such a problem are usually referred to as qualitative methods. Among them, very recently a new approach has been proposed for the case of bi-dimensional geometries and scalar field, based on the concept of joint sparsity and the solution of related inverse source problems. It is inspired by the fact that, whatever illumination conditions, the field scattered by the unknown (dielectric or metallic) object can be assumed as radiated by some (equivalent in case of dielectric object and induced in case of metallic) currents located on the unknown object s contour. Inspired from its flexibility and versatility with respect to the kind of experiments, in this contribution the rationale underlying the approach has been tailored and tested against the challenging and realistic case of three-dimensional geometry.